But, as Labor Leader Bill Shorten condeded, "no-one can predict what this senate will do".

Labor has promised to repeal the final two stages in government, if the Bill passes the upper house.

The decision sets up a showdown over tax at the July 28 'Super Saturday' by-elections, and also the next federal election, with Shadow Treasurer Chris Bowen urging the government to "bring this debate on".

Shorten said Labor's tax policy was "fairer and more responsible" and the government could guarantee tax cuts for over 10 million workers immediately if it was prepared to split the Bill.

The move puts the Turnbull government in a tight position, now having to rely on eight of 10 senate crossbenchers to get the plan passed through the Parliament. Picture: AAP. (AAP)